Tracial W*-Probability Spaces

In the setting of Complex Hilbert Spaces and Bounded Linear Maps: Standing Notation.

1. (Tracial W-probability spaces)**¶ A tracial W-probability space is a cyclic tracial operator algebra $(H,M,\Omega)$ such that $M=M''$, where $M''$ is the double commutant of $M$.

2. (Trace)¶ The trace $\tau_{M}$ of a tracial W*-probability space $(H,M,\Omega)$ is the trace of the cyclic tracial operator algebra $(H,M,\Omega)$.